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A060151
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Number of base n digits required to write n!.
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11
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1, 2, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 18, 19, 19, 20, 21, 22, 22, 23, 24, 25, 26, 26, 27, 28, 29, 30, 30, 31, 32, 33, 34, 34, 35, 36, 37, 38, 38, 39, 40, 41, 42, 43, 43, 44, 45, 46, 47, 47, 48, 49, 50, 51, 51, 52, 53, 54, 55, 56, 56, 57
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = 1 + floor(log(n!)/log(n)) = 1 + A039960(n) for n>1.
a(n) = 1 + log_n(A074182(n)) for n>1.
(End)
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EXAMPLE
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a(6)=4 since 6!=720, which in base 6 is 3200.
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MATHEMATICA
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Join[{1}, Table[IntegerLength[n!, n], {n, 2, 80}]] (* Harvey P. Dale, May 30 2014 *)
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PROG
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(PARI) default(realprecision, 10); for (n=1, 1000, if (n==1, a=1, a=1 + floor(log(n!)/log(n))); write("b060151.txt", n, " ", a)) \\ Harry J. Smith, Jul 02 2009
(Sage) [1] + [1 + floor(log(factorial(n))/log(n)) for n in range(2, 74)] # Danny Rorabaugh, Apr 14 2015
(Magma) [1] cat [1 + Floor(Log(Factorial(n))/Log(n)): n in [2..80]]; // Vincenzo Librandi, Apr 15 2015
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CROSSREFS
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Cf. A011776 for number of final zeros of n! written in base n.
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KEYWORD
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base,nonn,easy
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AUTHOR
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STATUS
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approved
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